Mondrian classifiers are built upon like-named Mondrian processes [1]}, which are multidimensional generalizations of Poisson processes. These can be interpreted as a recursive generative process that randomly makes univariate cuts partitioning the data space hierarchically into \(k\) -dimensional trees [2]}. A key feature of these processes is that they are self consistent: a Mondrian process operating on the partition of some domain (e.g. a subdomain) is equivalent to a Mondrian process operating on the subdomain directly, allowing simultaneous subprocesses. While Mondrian processes can be infinite, Mondrian trees designate the classifiers formed by finite Mondrian processes, akin to decision trees. Each split is constructed by randomly selecting a feature and threshold, where the probability of selection is proportional to the normalized range of values for the feature. Finally, Mondrian Forests are constructed by ensembling a group of Mondrian trees, akin to Random Forest classifiers.
